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As it was already mentioned in paragraph 5.2, a flux is a transport process of a distributed amount, each element of this flux drawing a pathway which is called the flux line (or flow line). According to the virtual model, this pathway is a continuous curve, and according to the systemic model, it is a concatenation of right-oriented (vectors) segments which represent a series of concatenated SEP.
The spatial configuration of the flow lines allows the classification of fluxes in two categories, which will serve only as asymptotic (virtual) bench-marks for the real fluxes.
Definition 5.3.1: The flux at which all the flow lines are open curves is named a totally open flux.
The amount which is transported by these fluxes cannot be localized in space. The totally open flux is able to transfer an amount from an object to another, provided that at least a part from these flow lines to intersect the area of the receiving object.
Comment 5.3.1: The word localized used in this paper means the definition of the spatial position of an object or of an amount which belongs to an object. Mathematically speaking, the position of an object is given by the position vector of that object against an external RS. The precise localization of the object requires that this vector to be invariant. But for the objects which are in motion (such as the fluxes), it is obviously that this vector vary continuously. In this case, we are dealing with a global definition of the domain in which the position variation of objects takes place and this global definition is possible if only the objects in motion are kept inside a known space with a definite position, as we are about to see next.
Definition 5.3.2: The flux at which all the flow lines are closed curves, confined inside a closed area Σ is named a totally closed flux.
The closed fluxes are also known as storage fluxes. For these fluxes, a closed area Σ may exist and this area contains all the flux lines inside it. This area confines a volume V, in which the entire scalar quantity M shall be found, this quantity representing the conveyance attribute of the closed flux. Based on the assumption that its position is determined in relation to a reference system, the area Σ allows the localization of amount M even if, in the inside, it is the object of a flux. Thus, as regards the outside section of area Σ, it might be stated that the volume V contains the amount M (but with a higher degree of non-determination than in the absence of the closed flux, without mentioning the inner static distribution of the amount M). The closed fluxes are the only method of localization and storage of some amounts which are able to exist only as fluxes (found to be in a continuous motion, such as, for instance, the photons).
A closed flux arises (is generated) as a result of a closure process, which means the forcing of the flux’s flow lines for their confinement only within a closed area Σ, and this closure can be done by using different means which shall be minutely described in the following chapters, but which are only listed in the present chapter:
Reflexion (special case - elastic collisions);
Refraction;
Rotation.
Comment 5.3.2: The closure of a flux is made, as it was already depicted, through the modification of the direction of the transfer rate so that the flow lines to become closed pathways in a confined volume. As we are about to see in the following chapters, the boundary surface of a medium does not allow the entire flux passing over; therefore, there will always be fractions of the initial flux which shall return into the origin medium (the reflected fluxes), otherwise speaking, this flux section shall be kept closed in this medium. As for the propagation fluxes, the same process of modification of the flux direction caused by the unevenness of the propagation medium’s parameters can lead to the propagation by curved flux lines which can be confined in a limited and definite volume. The closure through rotation is the most notorious closure method, knowing that any system which moves is equivalent with a flux; if a body has a known volume and it spins around a defined axis, all the pathways of the constitutive elements shall be curves confined in a definite volume, with the center in a point along this axis.
The totally closed or totally open fluxes are flux virtual models (theoretical, mathematical, ideal), most of the real fluxes being only partly open or closed, therefore, a certain flux is associated to a certain closure degree (complementary with the aperture one), that is a degree which represents the fraction of the closed flux lines from the total number of flux lines).
Comment 5.3.3: An eloquent example for displaying the closure degree of a flux is the case of a fluid which flows through a pipeline, in which case two types of flow exist: laminar and turbulent. The laminar flow in which the flux lines are theoretically maintained parallel is an example of a totally open flux, with a null closure degree. As for the turbulent flow, most of the flux lines are locally closed (the vortex phenomenon occurs), but there is an overall motion of all the swirls, an open flux, that is the common component of all the vortex vector fields, motion which determines the effective fluid flow through the pipeline. If a fluid fills a steady pot, any inner motion of the fluid (convective or turbulent) will represent a totally closed flux inside the pot volume.
The fluxes can also be divided in two groups according to a previous-mentioned parameter, called effective area (or section) (see definition 5.2.1.2). To not be mistaken with the capture cross section from the nuclear physics field, although they are interrelated notions.
Definition 5.3.3.: The flux with a constant effective section across its entire pathway is named isotom flux (synonym corpuscular flux).
The flux which outlines the translation motion of an EP, AT, of a missile, of an AB (for example, of a planet within a PS) as well as of an isolated photon, all of these being examples of isotom fluxes. All the other fluxes (non-corpuscular) make-up the class of fluxes with variable effective section (divergent or convergent fluxes depending on the sign of the effective section variation - plus or minus - on the covered distance unit).
If the Euler distribution of FDV is temporally invariant, we are dealing with stationary fluxes, otherwise, they will be non-stationary (time-variable).
From the point of view of the object which is involved in the flux and based on the process type, the fluxes can also be divided in displacement fluxes and propagation fluxes.
Definition 5.3.4: The flux which carries material objects along its entire pathway is named displacement flux.
The displacement fluxes carry material systems (abiotic, biotic or artificial) from one spatial location to another. The running water, wind, sea streams, people, goods and migratory animal flows, etc. are only few examples of displacement fluxes.
Definition 5.3.5: The flux which carries local state variations of a set of objects is named propagation flux.
The propagation fluxes carry local state modulations (mainly symmetrical variations around a reference value), the motion processes of the inner reference of the objects involved within the flux are cyclical (reversible) and strictly local processes. According to the above-mentioned facts, we may assert that the propagation fluxes carry processes. Within a propagation process, the elements with an altered state are not always the same but they are different every time. We shall return to the propagation process in the next chapter, after the medium’s definition shall be presented. These flux types are also abstract (ideal) models, the real fluxes containing components of both models in various ratios. Any propagation also involves a low local displacement (that is a local displacement flux), and the displacement fluxes imply state variations between the objects which are set in motion (which are therefore local propagation processes).
The equipartition of some vectors means an even spatial distribution of the application points and an evenness of the direction and modules of these vectors. Otherwise speaking, the direction and the module are common attributes on the set of the vectors distributed on the flux element, whereas the positions of the application points are specific (differential, disjoint) attributes of each vector.
Definition 5.3.6: The flux with null specific components of FDV modules and directions (all vectors have the same module and the same direction) is named totally coherent flux.
The totally coherent fluxes are therefore fluxes with FDV equipartition, the pathways of the application points (flux lines) are in this case clusters of parallel straight (or curved) lines. This flux type occurs only as an abstract model, the real fluxes might be only partly coherent. An example of this kind of flux is the elementary flux which was previously presented. The opposite situation is when FDV set of the flux has a null common component.
Definition 5.3.7: The flux with a null common component of FDV set is named totally stochastic flux.
Comment 5.3.4: The fact that the totally stochastic flux has a null common component of FDV set (or FQV), this means that there is no global motion (conveyance) process, which might lead the reader to the conclusion that there is no flux (namely, motion). Indeed, an overall flux does not exist, but a space-temporal distribution of the motion processes of the stochastic flux elements exist, therefore, there is also a flux (but a special type of flux with a null coherent component of the FDV set). The same fact (lack of an overall displacement of the flux elements) makes that the totally stochastic flux to be a totally closed flux.
The Euler distribution of a totally stochastic flux is a totally chaotic distribution (see par. 2.3). Neither this type of flux can really exist (it is also an ideal model), the real fluxes being only partly stochastic or otherwise speaking, for each real stochastic flux, there is an associated level of analysis (decomposition into domains) for which the common component of the flux elements set is no longer null (there is a local coherency, at the level of spatial or temporal domain).
Comment 5.3.5: For instance, in a gas where there is a partly coherent molecule flux (a flow) oriented in a given direction. If this flux would be entirely coherent, this means that no interaction would be able to exist on the direction normal on flow direction, so, the static pressure into the flow would be null. This is not allowed by the external flux molecules (not involved into the flux) which are ready to occupy the section with null static pressure, and they shall restrict the flux’s coherency degree up to a value which is always subunitary.
Although the real fluxes are neither totally coherent nor totally stochastic, the two basic flux types are very important for the objectual philosophy. We have seen that the inner T reference of a compound object is unique and common to all the object’s elements. The result is that the motion of this reference is evenly submitted to all of these components, which means that the inner T references of the components shall basically have the same motion (with the same modulus and direction), therefore, we are dealing with a totally coherent flux. This means that if a totally coherent real flux cannot occur in a medium, we might have in exchange totally coherent components (abstract) of these fluxes.
We shall see further on that not only T component of an isotom flux belongs to this category but also other components with invariant direction (for example, the normal and tangent component on a boundary surface or the components which are settled based on the directions of the axes of reference). We shall also notice that a coherent component of a real flux cannot simply vanish just like that, but as a result of an interaction process with a boundary surface, this component may turn into a stochastic one. There is also the reverse process of the transformation of a stochastic flux into a coherent flux (more exactly, into a flux with a totally coherent component), but this is also conditioned by the presence of a boundary surface.
Comment 5.3.6: For example, in case of the collision of a ball with a wall, the initial kinetic flux (impulse) is the totally coherent T component of the set made-up from the molecules of the ball’s membrane and the molecules of its inner pressure gas, all of them moving with the common translation velocity. At the moment of collision, there is a temporal interval in which the ball is deformed by the impact with the wall, but it does not move (the coherent component of normal translation at the wall is null). What has happened to the coherent flux? It’s simple! The initial coherent flux has turned into a stochastic flux (with a null coherent component), namely, into pressure and heat, and after that, very short temporal interval of immobility, the reverse process of turning the stochastic flux again into a coherent flux, but with an opposite direction (the ball reflection on the wall) to be initiated.
Therefore, we shall be dealing in the following sections with totally coherent or totally stochastic components of a flux, but these will be presented in a brief version, which means that a flux with a totally coherent component is referred to as a flux with a coherent component, a partly coherent flux, or coherent flux component. The same procedure is applied to the stochastic fluxes.
Comment 5.3.7: The concept of coherency has a broader meaning in this paper than the term used in the regular scientific language, and it is closely-connected to the notion mentioned in chapter 3, that is a common component of a set of objects. According to the definition of the totally coherent flux, the result was that, in case of the translation fluxes, if the directions and FDV modulus are the same (therefore, they are common on the vectors set), that particular flux is therefore totally coherent. However, the same coherency issue is valid for the rotation fluxes, but the difference is that, in this case, FDV directions cannot be invariant any longer, the modules also depend on the radius of gyration, but, the sense and the angular speed can be invariant. Therefore, the fluxes’ coherency criteria are different due to the motion type, but in case there are common components of SEP, there are also coherency degrees.
It is very important to be understood that a flux such as the stochastic one, contains a distributed motion of some objects within itself, but this motion is not perceptible from the outside of the space occupied by this flux, in the absence of a global, external component of the motion. This fact (inexistence of an apparent common motion) does not also mean the inexistence of the elementary fluxes, therefore, of the objects’ inner motion.
Comment 5.3.8: A classic example of this kind of flux is the chaotic motion of the molecules of a pressure gas inside a gas cylinder with a steady position, motion which obviously does not have a common component since the gas cylinder is motionless. The attribute which strictly depends on the intensity of the stochastic kinetic flux of the gas molecules is the pressure of the gas from the inside, pressure transmitted to the cylinder’s wall, where it causes a stretching effort of the cylinder casing material (another stochastic flux, but this time, it belongs to the cylinder casing’s atoms). As long as the intensity of the kinetic stochastic flux from the casing is under the breaking point of the cylinder material, the two fluxes (the stochastic one of the gas and the other stochastic flux of the casing atoms) will be in equilibrium on the bounding surface. When this limit is exceeded, the casing medium breaks, the equilibrium vanishes and the fractions of the cylinder walls will move together with the gas molecules towards quaquaversal directions (flux with a coherent component - the motion sense) as compared to the former position of the cylinder. None of these visible motions could not have been generated if the stochastic flux, occult but persevering, of the gas molecules would not have existed.
We are about to see in the following chapters that the introduction of these two basic concepts, of stochastic and coherent flux, allows us to have a new approach on notions, such as the equilibrium between forces, or the energy classification in the two components - kinetic and potential.
Copyright © 2006-2011 Aurel Rusu. All rights reserved.
